Question

Sketch the graph of a periodic function that is neither the sine nor cosine function. State the period of the function.

Answer 1

Graph: To help visualize the graph, students can use an applet which can be found at http://science.kennesaw.edu/~plaval/applets/SinCosDef.html. Using this applet, students can move a point along the unit circle. As the point moves, the graph of either the sine or the cosine function is traced. Students are strongly encouraged to use this applet to understand why the graph of y = sin x looks the way it does. The shape of the graph of sine is given by the figure below.
One can see in particular that the sine function repeats itself.
• Additional Properties: — y = sinx is an odd function, that is
sin(−x) = −sinx